size(200);
import graph;
path p=(0,11)..controls(4.99076300129,12.3815553558)and(9.27629321805,15.5957030184)..(12,20)
..controls(14.2402726292,23.6225727543)and(15.2699689517,27.8089385438)..(16,32)
..controls(16.6960503029,35.9959801748)and(17.1365982521,40.0362225711)..(18,44)
..controls(19.1551740317,49.3032701919)and(21.0615033772,54.4343065895)..(24,59)
..controls(26.9094514702,63.5205644624)and(30.861364845,67.4337017974)..(36,69)
..controls(39.3669510506,70.0262743354)and(43.0517911328,69.9029846467)..(46,68)
..controls(47.5969388456,66.9692215709)and(48.8192914491,65.486034834)..(50,64)
..controls(52.0740139625,61.3896547187)and(54.0747924394,58.7219500827)..(56,56)
  ..controls(56,56)and(56,56)..(56,56);
draw(p,linewidth(1));
draw(reflect((0,0),(0,1))*p,linewidth(1));

real t=maxtimes(p)[1];
pair P=point(p,t);

dot(P);
label("$(x,f(x))$",P,N);

draw(P--(P.x,0),dashed);
label("$x$",(P.x,0),S);
pair Q=(-P.x,P.y);

dot(Q);
label("$(-x,f(x))$",Q,N);

draw(Q--(Q.x,0),dashed);
label("$-x$",(Q.x,0),S);
label("$O$",(0,0),SW);
axes("$x$","$y$",Arrow());
